This answer may not be useful for the author (it's getting answered after a decade), but could possibly useful for others...
Try to run this code, you will get an idea of it
Suppose, the parameters are as such....
%%%%%%%%% CODE %%%%%%%%%%
% Parameters
L = 10; T = 10; H = 2;
k = 2*pi/L; sigma = 2*pi/T;
dx = L/50;
dt = T/20;
x = 0:dx:L;
t = 0:dt:T;
%%%%%%%% PLOTTING %%%%%%%%%%
figure(1)
for i = 1:length(t)
tt = t(i);
z = 0.5*H*sin(k*x-sigma*tt);
plot(x,z,'-ob','MarkerFaceColor','b')
yline(0,'-.r','M.S.L','LineWidth',2)
xlabel('x (m)')
ylabel('\eta (m)')
axis([x(1) x(end) -H*2/3 H*2/3])
drawnow
end
Hope this helped.
